Proceedings of the Ninth Pacific Conference on Earthquake Engineering

Building an Earthquake-Resilient Society

14-16 April, 2011, Auckland, New Zealand

Paper Number 192

Displacement-based seismic retrofit design for non-ductile RC frame structures using local retrofit interventions at beam-column joints

W.Y. Kam, S. Pampanin

Dept. of Civil and Natural Res. Eng., Uni. of Canterbury, Christchurch, New Zealand.

ABSTRACT: Seismic retrofit design using local retrofit interventions is often done using

piece-meal iterative approach, in which the local retrofit design and global structural

response are derived from iterative numerical models. Adopting a displacement-based

seismic retrofit approach and following capacity-design principles, the effects of local

retrofit interventions’ can be correlated to the expected global deformation responses.

Clearly acknowledging that displacement (or drift) is a better response parameter for

structural and non-structural damage, a displacement-based methodology gives a more

direct and rational seismic retrofit design. This paper will first introduce the concepts of

displacement-based seismic retrofit. Then, the design procedure is illustrated for two local

retrofit interventions for RC frames: a) selective beam-weakening retrofit, and b) post-

tensioning retrofit and fibre-reinforced polymer jacketing. The design procedure is then

verified using non-linear time-history analysis on a case study building retrofitted using

the two local interventions.

1 INTRODUCTION

1.1 Seismic retrofit design – current practice

Seismic retrofit using local retrofit interventions is often designed using a piece-meal iterative

approach, in which the local retrofit design and global structural response are derived from iterative

numerical models. The lack of understanding of the direct correlation between the global structural

performance enhancements and the associated local retrofit interventions encourages the widespread

use of global strengthening techniques (e.g. new shear walls, new braced-frames or seismic isolation)

(Thornton 2010).

The state-of-the-art guidelines on the seismic retrofit design outline several different approaches for

the seismic retrofit design of non-ductile reinforced concrete (RC) frames. The NZSEE guidelines

(2006) gives detailed force-based and displacement-based assessment procedures for RC buildings.

The force-based approach is developed from Park (1996) static force-based capacity approach while

the displacement-based approach is adopted from Priestley (1995). While both approaches focus on

achieving capacity design and the desirable ductile failure mode, the design approaches are not

correlated to any damage parameters (e.g. inter-storey drift, d). The NZSEE guidelines also do not

specify any guidance for a performance-based retrofit outcome but the guidelines provide values of

maximum allowable strains for various materials.

The American / ASCE approach is based on a performance-based seismic assessment using numerical

modelling (either elastic or non-linear and either static or dynamic analyses), consistent with the

practitioners’ approach for new building design (ASCE-SEI-41-06 2007). The performance of the

retrofitted structure, however, is assessed post-analysis and piece-meal iterative approach is necessary

to achieve an optimal retrofit design. For example, Chambers et al. (2007) describes an integrated

approach in which the ASCE-41 deformation acceptance criteria (e.g. plastic rotation for columns) are

incorporated within a non-linear dynamic analysis.

Adopting a displacement-based seismic retrofit approach and following the capacity-design principles,

local retrofit interventions’ effects can be correlated to the expected global deformation responses.

2

Acknowledging that displacement (or drift) is a better response parameter for structural and non-

structural damage (ASCE-SEI-41-06 2007), a displacement-based methodology gives a more direct

and rational seismic retrofit design (Priestley et al. 2007). This paper outlines a simplified

displacement-based seismic retrofit design procedure for regular non-ductile RC frames without

masonry infill walls for the conceptual/preliminary design. The design principles can be subsequently

extended for more complex structural forms. The design procedure is implemented on a case study

pre-1970s RC frames building and verified using non-linear time-history analysis.

1.2 Performance-based seismic retrofit response parameters

Performance-based seismic retrofit allows a greater flexibility in deciding building performance

objectives for seismic retrofit when compared to the design of new buildings. The required global

performance objectives can be correlated with the building structural and non-structural performance

levels (PLs) at the given levels of seismic intensities associated with specified return periods. This is

illustrated in Table 1, using the ASCE-41 terminology for the three global performance objectives: (a)

to maintain functionality of the building post-earthquake (Enhanced Rehabilitation Objective - ERO),

(b) to minimise fatalities (Basic Safety Objective (BSO)) or (c) to prevent collapse (Limited

Rehabilitation Objective - LRO).

Table 1. Seismic retrofit performance-objective matrix and performance levels based on the ASCE-41.

Operational PLImmediate

Occupancy PL Life Safety PL

Collapse

Prevention PL

50% in 50 years a b c d

20% in 50 years e f (100%NBS) g (67%NBS) h (33%NBS)

10% in 50 years i j (100%NBS) k (67-100%NBS) l (33%NBS)

2% in 50 years (MCE) m n o p (67-100%NBS)

Notes: PL = Performance Level

MCE = maximum

credible earthquake

%NBS - percentage of new building standard (NZSEE,2006)

Enhanced Retrofit Objectives (ERO)

Target Building Performance Levels

Ear

thq

uak

e

Haz

ard

Lev

el

ASCE-41 (2006) Table C1-1.

Rehabilitation Objectives

(adapted)

Limited Retrofit Objectives (LRO)

Basic Safety Objectives (BSO)

The different performance levels can be associated with displacement (or acceleration) demand

parameters, as well as non-failure of critical structural elements. Typical code provisions (e.g. ASCE-

41 and NZS1170 (2004)), specify inter-storey d limit of 2.0-2.5% for the design earthquakes as the

BSO (or 100% New Building Standard (NBS) in NZSEE terminology). The definition of the

deformation limit states can be also based on local structural elements deformation capacities (e.g.

moderate joint cracking at d = 1.0%) and/or non-structural elements deformation capacity (e.g.

moderate cracking of clay-brick infill walls at d = 0.5%) (ATC-58 2009).

In the 2004 New Zealand Building Act (DBH 2004) and the NZSEE guidelines, the adoption of the

quantifiable minimum standard of 33% of NBS is an attempt towards achieving LRO for critical

earthquake-prone buildings. It represents a reasonable balance of imposing a requirement for all non-

complying buildings (<100%NBS) and the existing status (in which only unreinforced masonry

buildings are retrofitted). However, achieving the minimum standard of 33% NBS does not imply

collapse prevention PL. The %NBS parameter defined in terms of lateral strength is yet to be

correlated to quantifiable performance (e.g inter-storey drift, damage etc). As such, it is of paramount

importance that in addition to achieving the minimum %33 NBS lateral capacity, ductile failure

mechanism (with sufficient ductility capacity) must also be attained for collapse prevention.

Alternatively, as shown in Table 1, different PLs (based on quantifiable damage parameter e.g. d) can

be specified for LRO, depending on the risk averseness of the owners and community. The d limit of

3.0-4.0% is typical given as the collapse prevention deformation limit state.

3

2 DISPLACEMENT-BASED SEISMIC RETROFIT DESIGN

2.1 Previous works

A direct displacement-based seismic design and assessment framework (abbreviated as DDBD) has

been previously introduced by Priestley and colleagues (1997; 2007). This approach was modified and

adopted within the NZSEE guidelines (2006). Within the NZSEE guidelines, the retrofit design is

attained by comparing the displacement capacity derived from non-linear pushover analysis against

the required displacement demand derived from a desired %NBS, the assumed ductility (µ) and the

associated equivalent viscous damping (ξsys).

Marriott et al. (2007) recently extended the DDBD approach for global strengthening of pre-1970s RC

frames with rocking walls retrofit solution. The added rocking walls retrofit limits the displacement

demand of the RC frames and prevents brittle failure modes. The target displacement limit is defined

at the start of the design procedure to correspond to the required PLs.

2.2 The proposed displacement-based seismic retrofit design

In principle, the proposed displacement-based retrofit design aims to determine the appropriate level

of retrofitted members’ capacities in the beam-column joints for a selected seismic retrofit

performance objective. The basic retrofit design strategy is to control the hierarchy of strength of the

beam-column joint to respect capacity design principles and to attain ductile flexural beam-hinging

failure mode.

Given the hierarchy of strength of the as-built beam-column connections in the RC frames, depending

on its typology, geometry, reinforcing details etc., various local retrofit techniques can be applied to

modify the hierarchy of strength within the M-N (moment-axial force) performance domain of the

connection to achieve the targeted performance. The proposed four-step procedure is illustrated in

Figure 1. The following sub-sections will highlight some of the key assumptions while further details

of the procedure are described in the Chapter 3 of ref. (Kam 2010).

3 STEP-BY-STEP RETROFIT DESIGN PROCEDURE

3.1 Step 0: Define the target performance objectives

The targeted performance objectives for the retrofitted building can be defined in relative to the

clients’ and building codes’ requirements, in terms of engineering demand parameters (such as d). It

is important to recognise that the elimination of non-ductile failure mechanisms and critical structural

weaknesses (e.g. irregularity) are more significant than the upgrade of the lateral force capacity alone.

In New Zealand practice (e.g. the NZSEE guidelines), the definition of seismic retrofit objective based

on the desired building base shear as a function of %NBS does not correlate well with expected

damages or global seismic response. As such, the %NBS parameter can be re-defined in terms of d

and the associated expected performance. For instance, the 33%NBS limit can be defined as LRO,

thus collapse prevention PL (d = 3.5-4.0%) in the design earthquakes (although this assumption is

principally incorrect as discussed in Section 1.2).

3.2 Step 1: Defining retrofitted-frames DDBD parameters

The DDBD parameters would define an equivalent single-degree-of-freedom (SDOF) elastic system to

the retrofitted RC frames, with the secant stiffness, Keff, to the target displacement, Δu, at the effective

height, heff, (Figure 1-step 1). The proposed retrofit design overcomes the two important difficulties of

the direct displacement-based seismic assessment: a) which element of the structure will first fail or

govern and b) what is the corresponding displacement profile of the building (Priestley et al. 2007).

By the virtue of the capacity design and the hierarchy of strength check of the beam-column joints, a

beam-sway mechanism can be achieved by design. As such the deformed shape, yield displacement,

Δy and damping-ductility (ξsys-µ) formulations for a flexural hinging beam-sway RC frame can be

4

adopted with minor modifications. Other parameters such as the effective mass, meff, and heff would be

a function of the building properties. The following expressions are used to generate the DDBD

parameters for a beam-hinging RC frame, but further detail is available in ref. (Priestley et al. 2007):

1

i

c

ui

H where

4

4

)4

1(3

4

n

nfor

H

H

H

H

H

H

n

i

n

i

n

i

i (1)

ii

ii

um

m

c

2

,

ud

ii

eff

mm

,

ii

iii

effm

hmh (2), (3) and (4)

where Hc is the inter-storey height at the base of the building; Hi and Hn are the height of level i and

roof height; i, i, and mi, are the displacement, shape factor and mass at level i.

The sys for the SW-retrofitted pre-1970s frames is hard to be determined at the preliminary stage.

Tentatively, a low, constant with ductility, value of sys = 12.5% can be assumed based on the

experimental results (Kam et al. 2010). The use of constant sys removes the need to estimate y and µ.

y may be difficult to be estimated for the SW-retrofitted pre-1970s RC frames with plain round bars

because the elastic deformations of the beams, columns and joints are hugely affected by the bond

capacity of the reinforcement. The use of constant sys may be non-conservative however for limited-

ductility design. Alternatively, the expressions for unbonded post-tensioned precast concrete systems

(sys ranges from 5-18%) can be used for SW retrofit solutions with external post-tensioning (Marriott

et al. 2007; Priestley et al. 2007).

3.3 Step 2: Determine the effective period and the required base shear.

The displacement response spectrum is used to derive the required effective period, Teff, corresponding

to the target design displacement, Δu,d, given the level of damping (sys). This is illustrated in Figure 1-

step 2, where the NZS1170:5 (2004) displacement hazard spectra is used in conjunction with three

performance levels: a) Limited Performance, LP (d =3.0%), b) Basic Performance, BP (d =2.0%)

and c) Advanced Performance, AP (d =1.0%). The 5%-damped elastic hazard spectra (Sd,elastic) are

reduced using a damping reduction factor, :

elasticdsysd SS ,}{ where 7.002.0

07.0

sys

(5) and (6)

where α = 0.25 and 0.50 for near field and far field design ground motions respectively. Thus, the

required based shear of the SW-retrofitted frames to achieve the previously defined target

performance-objective (in d) is calculated as Vb,req = Keff∙ Δu,d, where Keff is given by:

du

eff

eff

effT

mK ,

24 (7)

3.4 Step 3: Distribute the base shear and determine required members strength.

Given the Vb-req, the required flexural strength of beam hinges, Mb,req, can be determined using an

equilibrium approach (Priestley et al. 2007) or structural analysis with the Vb-req distributed up the

building height. The base shear is distributed in proportion to the floor mass and displacement, with an

additional 10% applied to the roof level to account for higher mode effects:

ii

roofroof

bbroofm

mVVF 9.01.0 at roof level

ii

iibi

m

mVF 9.0 at other level i (8) and (9)

A close form equilibrium distribution described by Priestley et al. (Priestley et al. 2007) is used:

5

istorey

istorey

eibV

VNV

,

,

,

and

building

cbii

eL

HVhFN

)6.0()( (10) and (11)

where Ne is the earthquake induced tension force in the ground columns (or sum of beam shears) and

Vstorey,i is the storey shear at level i. Vstorey,i is the cumulative applied distributed base shear force (Fi).

Lbuilding is the length of the building (sum of all bay lengths, Lb). The required beam flexural capacity at

each level i for the given d is then given by Mb,i, =Vb,i / Lb.

Figure 1. The proposed displacement-based seismic retrofit design for non-ductile RC frames.

The internal force distribution depicted in Figure 1-step 3 assumes the interior joints have sufficient

strength to develop Vc-int in the interior columns. If the interior joints have insufficient

6

strength/ductility/deformation capacities, then the interior joints will need to be retrofitted as well. In

the scenario where high d level (e.g. LRO or BSO) and a mixed beam/column-sway inelastic

mechanism are acceptable, the interior joints and columns are only checked for its ductility and

deformation capacities. Alternatively, the designer may opt to allocate higher column shear demands

to the exterior columns, in order to achieve a d performance level.

3.5 Step 4: Conversion of demand into a M-N performance domain.

Lastly, for the given Mb,i, at the exterior beam spans to sustain the beam-sway mechanism at a given

seismicity, Mb,i, can be converted into an equivalent column moment, Mc,bf,. Therefore, the Mc,bf, for

various performance levels can be projected and compared within the M-N performance space of the

retrofitted exterior beam-column joints (Figure 1-step 4). For the local retrofit design within the M-N

domain, in addition to the need to satisfy the hierarchy of strength requirement, it is also necessary to

satisfy the required flexural strengths of exterior spans’ beams, Mc,b-ext, to achieve the required

performance level (~Mc,bf,):

,,

,

2bfc

extbcM

M

and 22

,,

extbcbfc MM (12) and (13)

where Mc.bf is the provided beam flexural capacity (in terms of Mc). As explained in §2.4.1, the

following expression can be used to convert strength value of various failure modes into the equivalent

column moments (Mc). Mc,bs and Mc,j are the provided beam shear capacity and provided joint shear

capacity in terms of Mc.

b

c

c

b

bbfcL

H

H

LMM

'

',

c

c

b

bbsc HH

LVM ',

)(

',

jdhH

jdHVM

bc

cjh

jc

(14), (15) and (16)

where Hc, H’c, Lb and L’b are geometry parameters as illustrated in Figure 2.

Equations 12 and 13 assume the moment demands in the flexural hinges at the exterior spans have

sufficient ductility to allow moment redistribution during an earthquake. As one exterior span goes

into positive moment, the other will go into negative moment. Therefore, it is not unreasonable to

consider the sum of the exterior spans’ beam flexural capacity in computing the total contribution

from the exterior beam-column joints.

Figure 2. Equivalent column moment for various internal actions on exterior beam-column joints subassembly: a) Labelling; b) Internal action of exterior joint; c-d) Corresponding shear force and bending moment diagram of exterior beam-column joint subassembly.

7

4 SEISMIC RETROFIT DESIGN EXAMPLES

4.1 Case study building

A case-study six-storey three-bay RC frames building is designed to simulate the typical pre-1970s

mid-rise residential/commercial multi-storey building. Poor material properties, deficiencies in

reinforcement detailing and violation of capacity design philosophy are intently included in the

prototype structure. The global geometry and the 2nd

floor beam-column joint geometry are shown in

Figure 3a and further information is available in ref. (Kam 2010).

The columns are tapered from 15” (380mm) squares at first two floors to 14” (350mm) squares at

upper stories. The beams are 19.5” (495mm) deep by 13.75” (350mm) wide. Column stirrups are

typically 3/8” bars at 6” spacing (i.e. 9.5mm diameter at 150mm centres) while beam stirrups are 3/8”

bars at 8” spacing (9.5mm diameter at 200mm centres). Beam-column joints are not reinforced with

stirrups. The beam longitudinal bars are anchored into the exterior joints are using double 180° hooks

for both the top and bottom beam reinforcements. The reinforcing details for the exterior beam-

column joints are shown in Figure 3a (insert).

Figure 3. a) Geometry and structural detail of the case study RC frames building; b) Structural model of the prototype frame.

4.2 Numerical example of the seismic retrofit design

Table 2 summarises the DDBD parameters for the retrofitted six-storey case study building for a 2.0%

design d, based on Wellington seismicity (NZS1170 2004) with a peak ground acceleration (PGA) of

0.4g, Sp factor of 1.0 and an assumed system equivalent viscous damping ξsys of 10%. Soil class C and

no near-fault amplification are assumed. This is but one retrofit design example and depends on

different local retrofit interventions at the beam-column joints, different performance levels can be

attained.

Table 2. DDBD parameters for the retrofit design of the six-storey prototype RC frame for the Wellington seismicity, with Z=0.4g, Sp=1.0, soil class C, N=1..` and an assumed system viscous damping, ξsys=10%.

0.201 m 2.0 %

11.820 m 10.00

494 tonnes 934.6 kN

2.05 sec

Level 1-2 93.6 kNm

Level 3-6 46.4 kNm Interior L1-3 140 kNm

Exterior

Column 1 Interior Column Exterior L1-3 70 kNm

Column Axial Load Base: NG+Q+E 90.0 1620.1 Interior L4-6 119 kNm

Column Axial Load L3: NG+Q+E 348.3 946.1 Exterior L4-6 59 kNm

Column Design

Moment

SDOF design interstorey drift

kNmSDOF base overturning moment 2906.3

SDOF design displacement

SDOF effective height

SDOF effective mass

SDOF effective period

Beam Design Moment

SDOF equivalent viscous damping

SDOF design base shear (all frames)

8

The Sp factor is defined in the NZS1170:5 to account for additional conservatism in the design of

ductile structure (when compared to brittle structure). The Sp factor is a function of the structural

ductility, µ, ranging from 1.0 for µ = 1 (elastic structure) to 0.7 for µ ≥ 2. For displacement-based

retrofit design, a Sp of 1.0 is recommended and a more realistic ξsys can be used. However, in order not

to unnecessary penalise the displacement-based retrofit design, the Sp as a function of µ can be used

with a conservative estimation of the damping ξsys.

The case study building is retrofitted using two local retrofit interventions: (a) selective beam-

weakening retrofit (R1) and (b) post-tensioning retrofit and fibre-reinforced polymer jacketing (R2).

The local retrofit design at the exterior beam-column joints level must first satisfy the capacity design

requirements of weak beams, strong columns and joints. This is achieved by satisfying the correct

hierarchy of strength within each beam-column joint. The details of the design of the local retrofit

interventions are beyond the scope of this paper. Design expressions for the selective-weakening and

post-tensioning retrofit of pre-1970s beam-column joints (Kam 2010) and FRP jacketing retrofit (CEN

2006; Akguzel and Pampanin 2009) are available in literature. Figure 4a shows the details of the local

retrofit interventions used in the case study building.

9

18

27

36

45

54

63

72

81

91

20

40

60

80

100

120

140

160

180

0 0.5 1 1.5 2 2.5 3 3.5 4

Eq

ui.

Co

lum

n M

om

ent,

Mc,

bf(k

Nm

)

Ex

t. B

eam

Mo

men

t, M

b(k

Nm

)

Interstorey Drift (%)

6-storey, 3 bays retrofitted frame under

PGA=0.4g seismicity

BSO: Life-safety /

moderate damage PL

CP: Collapse

prevention PL

ERO:

Functional PL

R2 PT Joint + FRP Column Retrofit

R3 Beam SW+PT

R1 Beam SW-only Retrofit

As-built beam

ξ=10% Sp=f(µ)

ξ=15% Sp=1

R2 ~ 1.4%

R3 ~ 1.7%

R1 ~ 2.1%

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0Period (s)

Sp

ectr

al A

ccel

erat

ion

(g

ms-2

) .

T1 =

1.4

s

1.3

x T

1

7 FF Mean

0.4

x T

17 FF Min

7 FF Max

NZS1170:5 (FF)

NZS1170:5

(NF, r=10km)

NZS1170:5 (Wellington,

Z=0.4g, Soil C, Sp=1, R=1)

Far Field (FF)

Scaled Records

Figure 4. a) Schematic description of the three local retrofit solutions: R1, R2 and R3 designs; b) DDBD retrofit design for the prototype 6-storey 3-bay RC frames building under Wellington (PGA=0.4g) seismicity; and c) Spectral mean and maximum/minimum envelope for the scaled far-field records compared to the NZS1170:5 (2002) 5% damped design spectrum.

Figure 4b presents a series of design curves for several retrofit options, which relate the targeted

design d with the exterior beam-column joint’s Mc.bf. For example, the R1 retrofit solution, which

involves 50% beam bottom bars weakening, has a beam moment capacity, Mb of 88.5kNm (or

40.1kNm in terms of Mc,bf). This corresponds to a design d of 2.1% for the prototype building, under

the Wellington seismicity, a Sp factor of 1.0 and an assumed system equivalent viscous damping ξsys of

10%. Thus, Figure 4b illustrates how different local retrofit techniques, (beam-weakening, post-

tensioning, FRP jacketing etc) can achieve different retrofit performance objectives and limit states.

Figure 4b also highlights the large uncertainty introduced by the so-called Sp factor that is based on

structural ductility.

5 NUMERICAL VALIDATION OF THE DESIGN PROCEDURE

5.1 Numerical models

Non-linear time-history (NLTH) analyses are performed using the finite-element program

RUAUMOKO (Carr 2008). A Newmark-beta integration scheme with a 5% Rayleigh damping model

proportional to the initial stiffness is adopted. P-delta effects are ignored. Lumped mass and lumped

plasticity modelling are adopted, where inelastic deformations are limited to discrete inelastic

rotational springs in the joints, beams and columns. The numerical model of the prototype frame is

illustrated in Figure 3b. Further information of the numerical model is given in the Chapter 9 of ref.

(Kam 2010).

9

Careful attention is given to the correct representation of the beam-column joint connection, using

lumped plasticity rotational macro modelling approach (Pampanin et al. 2003). The Wayne-Stewart

hysteresis rule is used to model cyclic strength degradation, stiffness degradation and pinching

hysteresis behaviour, for the joint springs of the existing RC frames, as per Liu (2001) calibration.

As-built and retrofitted beam and column elements are modelled using the Giberson frame elements

with thin modified Takeda hysteresis (α=0.5, β=0). In the SW-retrofitted frames’ models, the inelastic

properties of the beam, column and joint elements are changed to account for the local retrofit

interventions. For the R1-retrofitted frame, the beam-weakening is modelled by a reduction of the

beam negative moment capacity and the beam initial stiffness. For the R2-retrofitted frame, the un-

bonded post-tensioning increases the beam and joint moment capacities, as well as the post-yield

stiffness of the beam. These effects of the local retrofit interventions are based on laboratory test result

observation (Kam et al. 2010).

5.2 Ground Motions

Seven scaled historical ‘far-field’ (without any directivity effect) strong ground motion records are

used in the analyses. Similar analyses with a suite of near-fault earthquakes were also carried out in

ref. (Kam 2010). The scaling of the earthquake records are done in accordance to the recommendation

of the NZS1170:5 (NZS1170 2004). The prototype building’s design site is assumed to be Wellington,

with the peak ground acceleration of 0.4g and a probability of exceedance of 10% in 50 years (R=1.0).

Soil class C is assumed. The response spectra of the scaled records are presented in Figure 4c.

6 RESULTS

6.1 Non-linear time-history responses

The non-linear time-history (NLTH) results are summarized in Table 3 and the average d responses

are presented in Figure 5. Figure 6 presents the mean of the peak response values of the global frame

and the mean peak rotations of each modelled component (i.e. joints, beams and columns) under the

seven far-field ground motions.

The as-built RC frame with slender columns and heavy infill partitions has a relatively long period

(T1~1.64s). The weakening of the beam reduced the beams stiffness and therefore softened and

lengthened the period of R1-retrofitted building (T1~1.73s), as one would expect from the beam-

weakening-only retrofit. The post-tensioning of the beam-column joint in R2-retrofitted building, on

the other hand, stiffened the overall structure (T1~1.57s).

The as-built frame performed poorly with the average maximum d of 2.43% at the 2nd

level, with the

joint shear deformation as the dominant inelastic mechanism, with moderate column hinging at the

base and almost negligible beam plastic deformation. The average joint plastic rotation demand,

exceeding 2.34% radians, suggested extensive joints damage, concrete spalling, column bars buckling

and incipient structural collapse. The non-ductile base column also had significant rotational demand

up to 1.18% radians.

The d at the effective height of the building (2.0%) was comparable to the design d of 2.1% for the

R2-retrofitted building. While no significant improvement was observed in terms of the global

displacement and d responses for the R1-retrofitted frame, the beam-weakening retrofit effectively

changed the dominant inelastic mechanism from a brittle joint shear failure to a relatively more ductile

beam flexural hinge, as evident from Figure 6. As the beams rotational demands were less than 1.75%

(in the maximum cases), ductile flexural response would have been achieved, as demonstrated in the

laboratory tests (Kam et al. 2010). The inelastic demands in the base columns and the roof knee joints

indicated moderate but repairable damage of these elements. Further retrofit interventions of these

elements may be necessary.

The R2-retrofitted frame showed the improvement in the d responses as well as in the components’

inelastic deformation demands. While the inelastic demands within the beam, joint and column were

10

more significant in the R2-retrofitted frame (see Figure 6c), the additional damping from these hinges

reduced the global d response marginally. The d at the effective height of the building (1.54%) was

comparable to the design d of 1.7%.

Table 3. Summary of non-linear time-history analyses results.

Buildings DesignMax inter-storey

drift (%)

Effective height

drift (%) *Roof Drift (%) **

As-built frame - 2.43% 2.08% 1.70%

R1-retrofitted frame ~2.1% 2.42% 2.00% 1.52%

R2-retrofitted frame ~1.7% 1.97% 1.54% 1.14%

Note: * Effective height of the building is 11.82m, as calculated based on the DDBD expressions.

** Roof drift = roof displacement / building height.

0 1 2 3 4 50

2

4

6

Interstorey Drift, %

Sto

rey

Mean +

Mean -

Maxima

NLEV

0 1 2 3 4 50

2

4

6

Interstorey Drift, %

Sto

rey

Mean +

Mean -

Maxima

FS

0 1 2 3 4 50

2

4

6

Interstorey Drift, %

Sto

rey

Mean +

Mean -

Maxima

BLR1 R2

As-built

Figure 5. Average of peak inter-storey drift, d, responses: Column: a) As-built frame; b) Beam-weakening only R1 retrofitted-frame; and c) Full SW R3-retrofitted frame.

0% 20% 40% 60% 80% 100%

6

5

4

3

2

1

Sto

rey

Percentage of plastic deformation (%)

Joint

Beam

Column

0% 20% 40% 60% 80% 100%

6

5

4

3

2

1

Sto

rey

Percentage of plastic deformation (%)

Joint

Beam

Column

0% 20% 40% 60% 80% 100%

6

5

4

3

2

1S

tore

y

Percentage of plastic deformation (%)

Joint

Beam

Column

R1-retrofitted

frame

As-built

frame

R2-retrofitted

frame

Figure 6. Decomposition of the plastic deformations for the three models under far-field ground motions: a) As-built; b) Beam-weakening only retrofit (R1); and c) External post-tensioning retrofit (R2).

The d responses were generally higher than the average drift at the effective height, as the NLTH

responses’ deformed shape was not the beam-sway deformed shape assumed in the displacement-

based retrofit design procedure. As illustrated by the distribution of d up the building height in Figure

5, higher deformation demands were observed in the lower two to three storeys. One critical reason for

this was the simplified design adopted for this study, in which the retrofitted beams and the columns

capacities were not varied up the building height. The design assumed the ductility demands on the

plastic hinges could be redistributed in the retrofitted frames during the earthquakes.

6.2 Limitations

While the aim of attaining ductile beam flexural failure mode, as per the capacity design philosophy

was successful, evident from the results shown in Figure 6, the global inter-storey d responses

exceeded the design expectations in some cases.

The deformed shape of the building depends heavily on the assumptions of the distribution of the

inelastic mechanisms. The use of a constant beam flexural strength up the building elevation and the

reliance on possible moment redistribution may not be suitable for the seismic retrofit design of non-

ductile RC frames. As shown in Figure 5, this design configuration leads to significantly higher

inelastic demand at the lower storeys and limited inelasticity at the upper storeys. This results in a less-

11

than-expected flexural inelastic action and damping, and therefore, higher global responses in terms of

displacements and drifts.

Further studies in correlating the retrofit design to the deformed shape of the retrofitted frame

buildings are necessary to refine the design procedure.

7 CONCLUSIONS

A displacement-based design procedure to derive the lower bound of required retrofitted elements

capacities given a targeted performance level is presented. Two local beam-column joint retrofit

interventions, namely a) selective beam-weakening retrofit, and b) post-tensioning retrofit and fibre-

reinforced polymer jacketing, are used to demonstrate design procedure for a case study pre-1970s RC

frames building.

This conceptually straight-forward retrofit design approach can be implemented in a spreadsheet

program for preliminary retrofit design. The advantage is a direct correlation with seismic

performance response parameters such as the d and related structural/non-structural damages to the

retrofitting design decisions. Incorporating the local seismic retrofit interventions design from a global

level at the conceptual stage allows for a more efficient if not economical retrofit solution.

However, the NLTH results have shown the limitations of the some of the assumptions including the

deformed shape profile and the moment redistribution of the retrofitted frames. Further parametric

analyses on different building configurations and scenarios are required to improve the robustness of

the simple design approach.

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